Massive neutrinos and primordial nucleosynthesis

The effect of massive ($m\ge 0.1$ MeV) neutrinos on primordial nucleosynthesis is calculated. It is shown that the effect on big-bang helium (deuterium) production of a 0.1-10 MeV (0.1-25 MeV) neutrino is more significant than the effect of a massless neutrino. If a lower bound on the present baryon-to-photon ratio is placed from determination of the virial mass in binaries and small groups of galaxies (where massive neutrinos are not expected to contribute to the virial mass) or from the requirement that big-bang nucleosynthesis not overproduce ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, then limits may be placed on the masses of any neutrinos present at nucleosynthesis.